When Beyoncé's Mrs Carter Show world tour arrived in the UK last spring, it had everything a high-end pop diva spectacle could want – an obsession with Marie Antoinette, sparkly purple catsuits, truly innovative lighting and video – and, of course, the titular Mrs Carter herself, the 17th most powerful woman in the world according to Forbes magazine, dangling off a fish-hook in mid-air.

There was also the not inconsiderable catalogue of hits stashed under her crinoline, most of which were stylishly remodelled for the occasion. The only thing that was lacking last year – other than daughter Blue Ivy on backing vocals and hubby Jay-Z bringing Beyoncé a cup of hot lemon water with honey in it – was the new album that tour was supposed to be touring.

Beyoncé (the "visual" LP) arrived very suddenly in December, sending critics into raptures, breaking iTunes records, outselling all other American pop divas in the fourth quarter and quite possibly revitalising the entire album format. You had to buy the whole thing in those first days, no downloading single tracks. For the closing Stateside Mrs Carter shows of 2013 (the second highest-grossing tour of 2013), Beyoncé stuck just one new song into the set list: XO, the love song to her fans.

Good as Mrs Carter was, you wouldn't normally review the same tour twice in a national newspaper. But this Glasgow gig kicks off a whole new Mrs Carter leg. This is the Mrs Carter Show Mk II, and the swanky SSE Hydro is glowing pink from the inside, perhaps in anticipation of new Beyoncé songs. And while much remains from Beyoncé's last jaunt around our parts – the impressive silhouette sequence, Les Twins (her French twiglet dancers) and If I Were a Boy interpolating the Verve's Bittersweet Symphony – a handful of actual new songs do receive their world live premiere (if you're not counting the Grammys and the Brits). It is, emphatically, not the same gig twice.

It even starts differently, with some disembodied portent: clanking and atmospherics that resolve themselves into Haunted, one of the more nagging and subtle melodies from Beyoncé. Beyoncé glides on in a glittery gown which transforms into a catsuit in time for the next song: the stand-out Drunk in Love, performed while slung wantonly across a chair. At the Grammys last month, Beyoncé did it alongside Jay-Z. A little disappointingly, Mr Carter is not on hand tonight to bear witness to one of the classier displays of erotic abandon. Most pop and R&B singers have to produce a simulacrum of arousal in their performances; quite often it's mechanistic and boring. Remarkably, though, the ecstatic yelps of Beyoncé's ad libs in Drunk in Love make you feel like she actually got tipsy and had the hots for her husband. There is a great deal of raunch to this tour – then, and now – but Beyoncé's cavorting feels a cut above the usual knee-jerk flaunt'n'grind of most other performers.

Later, a costume change interlude finds her discussing sensuality and power via a voiceover. We're in Madonna territory here – advanced sexy studies, the post-feminist module – but, crucially, it elicits none of the crude smirking that accompanied Madonna's Sex book so long ago. Blow – probably the most sexually explicit song on Beyoncé, among many – comes served in a disco-era wrap. The LED screen projection of Pac-Man eating his way through some cherries before keeling over is funny rather than risible.

Madonna always shirked the feminist label: Beyoncé, by contrast, embraces it, even as she pole dances with brio. A passage from a TEDx talk on women and development in Africa given by the writer Chimamanda Ngozi Adichie was one of the talking points of Beyoncé's album when it came out in December. Tonight, Flawless (the song which houses the sample) is introduced with significant excerpts from Adichie's feminist broadside written in giant lit-up capitals: Beyoncé's affiliation could not be plainer. "Feminist," the lights spell out: "a person who believes in the social, economic, and political equality of the sexes." But what happens next? The song interpolates a bit of Bow Down (Bitches) – the taster track that prefaced the arrival of Beyoncé; a song which deploys a term that is either insulting to all women, or just to bitches (a category that can include men, if you move in hip-hop circles). If you were, say, 18, like the girl called Julia to whom Beyoncé sings Happy Birthday at the end, you might be forgiven for being somewhat confused by this women's mag version of feminism: the "sexy powerfulness" tendency, rather than the school of thought that defends the right not to have to behave like a stripper. But it's cheering all the same.

There is no question as to Beyoncé's own powers. She can stop and start her all-female band – including backing vocalists and a horn section – with a click of her fingers, and keep climbing octaves until you think her lungs are about to jump out of her chest. She sings (with a range that only gets wider and deeper with every tour) and dances (flawlessly) for more than one and a half hours. Beyoncé and her team rehearsed all night on Monday into Tuesday morning to make sure everything in this new and improved Mrs Carter Show was up to scratch. It is.

Following the release of Beyoncé's secret album, Aaron Hicklin is offered unprecedented access to the people who know her best. With these insights he joins the star on tour and asks her about feminism, sexuality and giving her fans what she wants…